What can or can't be estimated in branching and related processes?
type: Item
instance of: scholarly article
title: What can or can't be estimated in branching and related processes?
zbMATH Open document ID: 0687.62071
DOI: 10.1016/0304-4149(89)90094-X
author: Ellen Maki
author: Philip McDunnough
published in: Stochastic Processes and their Applications
publication date: 1989-01-01T00:00:00Z
review text: This note compares the incompletely observed random walk and Galton- Watson branching tree. For the random walk, parameters not completely determined by the first few moments of the underlying distribution cannot be consistently estimated. A similar result holds for the branching tree with the observations now being sums of family sizes. In the case where the offspring distribution belongs to a power series family, it is possible to obtain the maximum likelihood estimators from an approximate likelihood. The estimates are the same as when individual family sizes are observed.
reviewed by: J. Gani
Mathematics Subject Classification ID: 62M05
zbMATH DE Number: 4126528
zbMATH Keywords: consistent estimation
zbMATH Keywords: incompletely observed random walk
zbMATH Keywords: Galton-Watson branching tree
zbMATH Keywords: sums of family sizes
zbMATH Keywords: offspring distribution
zbMATH Keywords: power series family
zbMATH Keywords: maximum likelihood estimators
zbMATH Keywords: approximate likelihood
MaRDI profile type: Publication
cites work: Q4191474
cites work: Q4097679
cites work: Consistent estimation in partially observed random walks
cites work: Exact distributions of kin numbers in a Galton-Watson process
cites work: Q4157846
cites work: On the non-existence of consistent estimates in Galton-Watson processes
cites work: Sampling a branching tree
cites work: Application of the Galton-Watson process to the kin number problem
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description: scientific article; zbMATH DE number 4126528